328 reputation
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location Brazil
visits member for 1 year, 11 months
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I'm a Computer Science undergraduate who likes theory more than practice (even though I do enjoy programming).

The reason for my choosing this username is that some of my characteristics remind me of those of a Turing machine. For example, I think I often face difficulty understanding concepts that aren't presented to me in a simple, step by step, logical way, but I feel that if a concept is broken down into sufficiently simple parts, then I can understand it, as long as I'm provided with sufficient time, health, and so on*. This characteristic of mine reminds me of how simple the things a Turing machine can do are. You can't ask it to give you the result of "5 to the power of 8" directly; you'd have to break this down into very simple steps for it to be able to accomplish the task.

*The expression "and so on" trivializes my claim, in the sense it, for example, allows one to add contradictory conditions (like health and complete lack of health), thus making "I can understand foo given the conditions bar" vacuously true. That's not my intention. I just haven't been able to think of a set of conditions whose conjunction would be a sufficient condition for me to understand something broken into simple parts. If I ever think of a way to express myself in a more precise way in this regard, I'd definitely change that, as long as I have access to the internet, I remember I have written it, and so on... Oh, wait, here we go again...

I find the distinction between abduction and deduction** useful to contrast science (physics, biology, chemistry, ...) with mathematics: scientists rely heavily on abduction to convince (themselves and) other scientists of what they think is true, whereas mathematicians use deductive arguments ("proofs") as the primary procedure for convincing each other. Note, however, that it is in the way of convincing others in the same field that I'm claiming scientists and mathematicians are different. I have said nothing on how scientists and mathematicians conceive the claim they'll try to convince others of in the first place. (I think I have nothing to say in that respect.)

I feel I'm very limited in my ability to "do the scientist's job" and to try to find the "best" explanation for a given observation. On the other hand, I feel comfortable writing down mathematical proofs. (The difficulty in the process of solving a mathematics exercise is, to me, in finding what claims I must prove and in figuring out why the claims to be proved are true.)

**Well, the link also explains inductive reasoning, but it seems to me that inductive reasoning is a special case of abductive reasoning and that, for that reason, one shouldn't speak of the distinction between deduction, abduction and induction, but rather of two distinctions: that between the first two, and that between induction and non-inductive abduction.

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